The Fiorentina captain was found dead in his hotel room at the weekend, just hours before his side's game against Udinese, which was subsequently postponed along with every other Serie A match that day.
An autopsy revealed that Astori died of a cardiac arrest by natural causes, but Paris Saint-Germain full-back Alves caused controversy with his comments regarding the incident in a press conference on Monday.
"We were not disturbed too much because we did not know him very much, I am sorry for his family," the defender told reporters when questioned over Astori's death.
"In the world every day thousands of children who do not receive much attention die of hunger and they are just as important. We all have to die sooner or later because we are passing through."
Balotelli subsequently vented his anger on his Instagram story, criticising the Paris Saint-Germain fullback's comments.
"He should've just passed on his condolences and that's it, not talk rubbish. You cannot make those comments when faced with someone's death. He said things that had **** all to do with anything," he said.
"Astori, by the way, was a good guy. Unfortunately, I can't go to the funeral on Thursday because I have a training session, otherwise I would've got in the car and attended."
Balotelli and Astori previously played together for the Italy national team.